Winter in Wooster: Answering the Hypotheticals No One’s Ever Asked

Image by Alia-Moosvi via DeviantArt
Caroline Ward, S&E Editor

What’s the biggest snowman you could make before the snow collapsed in on itself?

Let’s start with a hypothetical. Say you are an undergraduate college student at a generic liberal arts college in the Midwest. And say you are starting to feel a little lonely – it’s okay, we all do. And let’s say there’s a lot of snow at the moment, and you’re struck with sudden inspiration. A snow friend!! Great idea. You pack a ball and start rolling. For experiment’s sake, you’re in an endless field of snow, so you can roll this snow ball for as long as you want to (or physically can). You start to roll. At first things are slow, but as you roll your ball through the perpetual snow, it starts to form a thick band of snow around the original snowball. As you begin to form your snow friend, you realize that the snow is now packing in on itself in the middle, and it might even lose some volume. When you were first rolling the snowball, there was far less gravity from the outer snow shell pushing in on the center, but as the mass of the outer shell grows, the inner shell will become more tightly packed, thus reducing its volume and increasing its density. The cycle will repeat as the ball grows larger, until finally your snowman is left bruised and battered with a heart of solid ice. This is no way to make a friend. No wonder you are lonely.

How much snow does it actually take to fill up the arch?

This, on the other hand, is a deeply practical question for any enterprising undergraduate, but before we dive too deep into the very legitimate mathematical theory of this section, let us first define specifically what we’d like to measure. What does it mean to “fill” the arch? Now, the historical record will show that within the decades-long tradition of filling the Delmar Archway, to successfully “fill” the arch means that some point of the constructed snow pile/wall makes contact with the top of the arch’s ceiling. Using this definition, the amount of snow required to “fill the arch” is much smaller than the volume of the actual arch. However, what about filling the entire thing? To consider this, let’s take a trip back in time to the roots of the tradition. It was the 1960s, and the College took up the entirety of Kauke Hall. The decade was different, but the Ohio cold was not, and winter here was still a bitter wasteland. At the time, Kauke Hall had two main points of entry – both inside the archway – and to block those meant no real access to the building: a sure-fire snow day. Defined this way, to successfully “fill the arch” is to fill it, more or less, in its entirety. Although clever readers may have caught on that this requires far more snow than is actually needed, let’s ask the question anyway: how much snow does it take to fill up the arch in its entirety? Now that we’ve figured out our question, the solution is simple. Well, almost. I couldn’t get a clear answer on this, so instead, we’ll turn to tried and true guess-timation. Let’s say my friend is 5’, and she is standing in the archway. If I were to measure, it would seem that the height of the arch is about 3.5 (my friend), with a width of 3(friend), and a length of 7(friend). So let’s say the arch is roughly 17.5 ft. by 15 ft. 35 ft. This is a volume of 9187.5 cubic feet! To put 9187.5 cubic feet into context, that’s a lot!

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